Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths, radii and Young's modulus of wires $A$ and $B$ are $r, 2r$ and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if ratio of increase in their corresponding lengths is $1/6r^2$. The mass of block $Q$ is $3M$.

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

A wire of length $2\, m$ is made from $10\;c{m^3}$ of copper. A force $F$ is applied so that its length increases by $2\, mm.$ Another wire of length 8 m is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by......... $cm$

 A steel wire is stretched with a definite load. If the Young's modulus of the wire is $Y$. For decreasing the value of $Y$

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus is:

A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$